I'm 700kms south of Beijing and we've got a forecast of rain, then a max of 2-3 degrees. You'll absolutely going to need mountaineering gear on your bike with a balaclava under the helmet. Then you'll not get much more than two hours before it's unbearable. I'd head south by train or plane and start there.

Also wealthier cities generally have less bikes available and bans/silly expensive rego. Do yourself a favor and get out of Beijing or any mega city to a 1st or 2nd tier provincial city such as Jinan, you might be able to find a Qingqi dealer who'll rego the bike for you for a reasonable price, they might even have something in stock new. You almost certainly won't find anything for 3000RMB, other than a 3 year old 125cc at best.